निम्नललिखित व्यंजकों को सरल कीजिएः
(i) `(5+sqrt(7)(2+sqrt(5))` (ii) `(5+sqrt(5))(5-sqrt(5))`
(iii) `(sqrt(3)+sqrt(7))^(2)` (iv) `(sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))`

Explanation

(i) `(5+sqrt(7))(2+sqrt(5))=10+5sqrt(5)+2sqrt(7)+sqrt(35)`
(ii) `(5+sqrt(5))(5-sqrt(5))=5^(2)-(sqrt(5))^(2)=25-5=20`
(iii) `(sqrt(3)+sqrt(7))^(2)=(sqrt(3))^(2)+2sqrt(3)sqrt(7)+(sqrt(7))^(2)=3+2sqrt(21)=7=10+2sqrt(21)`
`(sqrt(11)-sqrt6))(sqrt(11)+sqrt(7))=(sqrt(11)^(2)-(sqrt(7))^(2)=11-7=4`